Question

For your job as the business reporter for a local newspaper, you are given the task of putting together a series of articles that explains the power of the time value of money to your readers. Your editor would like you to address several specific questions in addition to demonstrating for the readership the use of the time value of money techniques by applying them to several problems. What should be your response to the following memorandum from your editor?

TO: Business Reporter

FROM: Perry While, Editor, Daily Planet

RE: Upcoming series on the Importance and Power of the Time Value of Money

In your upcoming series on the time value of money, I would like to make sure you cover specific points. In addition, before you begin this assignment, I want to make sure we are all reading from the same script, because accuracy has always been the cornerstone of the Daily Planet. In this regard, I would like responses to the following questions before we proceed:

a. What is the relationship between discounting and compounding?

b. What is the relationship between the present-value factor and the annuity present-value factor?

c. (1) What will $3,700 invested for 5 years at 14% compounded annually grow to?

(2) How many years will it take $240 to grow to $530.56, if it is invested at 12% compounded annually?

(3). At what rate would $1,700 have to be invested to grow to $148,341.65 in 27 years?

d. Calculate the future sum of $1,800, given that it will be held in the bank for 16 years and earn 8 percent compounded semiannually.

e. What is an annuity due? How does it differ from an ordinary annuity?

f. What is the present value of an ordinary annuity of $1,600 per year for 8 years discounted back to the present at 14%. What would be the present value if it were an annuity due?

g. What is the future value of an ordinary annuity of $1,600 per year for 8 years, compounded at 14%? What would be the future value if it were an annuity due?

h. You have just borrowed $140,000, and you agree to pay it back over the next 15 years in 15 equal end-of-year payments plus 10 percent compound interest on the unpaid balance. What will be the size of these payments?

i. What is the present value of a $1,900 perpetuity discounted back to the present at 14%

j. What is the present value of a $1,700 annuity for 10 years with the first payment occurring at the end of year 10 (that is, ten $1,700 payments occurring at the end of year 10 through year 19) given a discount rate of 16%

k. Given a 7% discount rate, what is the present value of a perpetuity of $1,800 per year if the first payment does not begin until the end of Year 10.

Answer 1

a	Compounding is the method to determine the future value of present investment
	Discounting is the method to find the present value of future amount received
b	The present value factor is the discounting factor of the discount rate of a particular year
	Annuity present value factor is the sum of the present value factor
c	3700*((1+0.14)^5)	(1.14^5)*3700	7124.033955
2)	240*((1+0.12)^n)=530.56
	1.12^n = 530.56/240
	1.12^n = 2.210667
	Solving the above would give around 7 years
3)	1700*((1+x)^27)=148341.65
	we can find the rate by using the trail and error method
	Assuming the rate is 14% we get
	1700*(1.14^27)
	58462.83984
	Assuming the rate is 18% we get
	1700*(1.18^27)
	148341.6545
d	1800(1+0.04)^32
	1800*(1.04^32)
	6314.505744
e	Annuity due is the repeating payment that is made at the beginning of each year. In ordinary annuity the payments are made at the end of each year
f	Year	Annuity	Discount Factor @ 14%
	1	1600	0.877192982	1403.509
	2	1600	0.769467528	1231.148
	3	1600	0.674971516	1079.954
	4	1600	0.592080277	947.3284
	5	1600	0.519368664	830.9899
	6	1600	0.455586548	728.9385
	7	1600	0.399637323	639.4197
	8	1600	0.350559055	560.8945
				7422.182
	The present value of ordinary annuity is $7422.18
	Year	Annuity	Discount Factor @ 14%
	0	1600	1	1600
	1	1600	0.877192982	1403.509
	2	1600	0.769467528	1231.148
	3	1600	0.674971516	1079.954
	4	1600	0.592080277	947.3284
	5	1600	0.519368664	830.9899
	6	1600	0.455586548	728.9385
	7	1600	0.399637323	639.4197
				8461.288
	The present value of annuity due is $8461.29
i	1900/1.14
	1666.666667
	The present value of annuity is $1666.67
j	Year	Annuity	Discount Factor @ 16%	Present Value
	10	1700	0.2267	385.36
	11	1700	0.1954	332.21
	12	1700	0.1685	286.39
	13	1700	0.1452	246.89
	14	1700	0.1252	212.83
	15	1700	0.1079	183.48
	16	1700	0.0930	158.17
	17	1700	0.0802	136.35
	18	1700	0.0691	117.55
	19	1700	0.0596	101.33
				2,160.55
	The present value of annuity would be $2160.55